Chapter 8
The Displacement Method
The displacement method is a powerful method for analysis of statically
indeterminate frames subjected to different external exposures.
The displacement method is effective especially for analyzing sophisticated
structures with a large number of redundantconstraints. Two forms of the displace-
ment method are applied in structural engineering. One uses the expanded form and
the other the canonical form equations. In this book only canonical form will be
considered.
The displacement method was introduced in 1826 by C. L.Navier(1785–1836).
A.Clebsch(1833–1872) presented the displacement method for trusses in expanded
form (1862). This method was further developed by H.Manderla( 1880 ), E.Winkler
( 1892 ), and O.Mohr( 1892 ). The application of the displacement method to frames
was presented by A.Bendixen( 1914 ) and was called the slope-deflection method.
Later this method was developed and presented in canonical form by A.Ostenfeld
( 1926 ). A significant contribution in the development of the canonical form was
added by S.Leites( 1936 ).
The displacement method in canonical formis brought to elegant simplicity and
contains a deep fundamental idea. This form offers a unified and rigorous conve-
nient algorithm for analysis of different statically indeterminate structures. Among
them are the single- or multispan as well as multileveled frames with deformable
or infinitely rigid crossbars, etc. Canonical form can be effectively applied for the
analyses of structures subjected to different loads, temperature changes, settlements
of supports, and errors of fabrication. Application of the displacement method in
canonical form for the construction of influence lines is very effective and leads to
a simple and clear procedure.
Moreover, the displacement method in canonical form is a very effective tool for
the special parts of structural analysis,such as stability and structural dynamics.
8.1 Fundamental Idea of the Displacement Method......................
Analysis of any statically indeterminate structure by the displacement method in the
canonical form begins with determining the degree of kinematical indeterminacy.
I.A. Karnovsky and O. Lebed,Advanced Methods of Structural Analysis,
DOI 10.1007/978-1-4419-1047-98,cSpringer Science+Business Media, LLC 2010
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